School of Mathematics and Statistics - Theses
Now showing items 1-10 of 179
Singular vectors for the WN algebras and the BRST cohomology for relaxed highest-weight Lk(sl(2)) modules
This thesis presents the computation of singular vectors of the W_n algebras and the BRST cohomology of modules of the simple vertex operator algebra L_k(sl2) associated to the affine Lie algebra of sl2 in the relaxed ...
Missing data analysis, combinatorial model selection and structure learning
This thesis examines three problems in statistics: the missing data problem in the context of extracting trends from time series data, the combinatorial model selection problem in regression analysis, and the structure ...
Exact solutions in multi-species exclusion processes
The exclusion process has been the default model for the transportation phenomenon. One fundamental issue is to compute the exact formulae analytically. Such formulae enable us to obtain the limiting distribution through ...
Yang-Baxter integrable dimers and fused restricted-solid-on-solid lattice models
The main objects of investigation in this thesis are two Yang-Baxter integrable lattice models of statistical mechanics in two dimensions: nonunitary RSOS models and dimers. At criticality they admit continuum descriptions ...
Consolidation problems in freight transportation systems: mathematical models and algorithms
Freight distribution systems are under stress. With the world population growing, the migration of people to urban areas and technologies that allow purchases from virtually anywhere, efficient freight distribution can be ...
Models of infectious disease transmission to explore the effects of immune boosting
Despite advances in prevention and control, infectious diseases continue to be a burden to human health. Many factors, including the waning and boosting of immunity, are involved in the spread of disease. The link between ...
Quantitative Epidemiology: A Bayesian Perspective
Influenza inflicts a substantial burden on society but accurate and timely forecasts of seasonal epidemics can help mitigate this burden by informing interventions to reduce transmission. Recently, both statistical ...
Integrated Wishart bridges and their applications
This thesis focuses on the study of Wishart processes, which can be considered as the matrix-valued square-root processes. In mathematical finance, the square-root processes find applications in interest rates modelling ...
Coset construction for the N=2 and osp(1|2) minimal models
The thesis presents the study of the N=2 and osp(1|2) minimal models at admissible levels using the method of coset constructions. These sophisticated minimal models are rich in mathematical structure and come with various ...
Sparse composite likelihood approaches for high dimensional data
The idea of the likelihood function, which plays an important role in the his- tory of statistics, has been widely used in many areas in parametric statistics. Composite likelihood approaches are useful tools to make ...